[R] A Math question

[rex.dwyer at syngenta.com]

If y'all want to discuss this more, do it somewhere else, please.
This has little to do with R except that both depend on Peano's Axioms.

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of JLucke at ria.buffalo.edu
Sent: Tuesday, February 15, 2011 12:46 PM
To: Kjetil Halvorsen
Cc: r-help at r-project.org; r-help-bounces at r-project.org; Maithula Chandrashekhar
Subject: Re: [R] A Math question

Kjetil et al,
Unlike finite sums, infinite sums are not commutative. To have
commutativity, one must have absolute summability, that is, the sum of the
absolute values of the terms must be finite.  If one has absolute
summability, the infinite sum exists and is unique. This sum is not
absolutely summable and thus undefined.   If one does not require
commutativity, then the order of the summation must be specified.  The
order is often implicitly assumed to be the order of the integers. The sum
of the negative integers is negative infinity, the sum of the positive
integers  is infinity, and the sum of these two sums is undefined.
However, Riemann's rearrangement theorem shows that the terms can be
re-ordered to yield any sum whatsoever.  In particular, if one creates
pairs of terms consisting of  a positive integer and its negative, then
the infinite sum is zero.   So the unique sum is undefined; otherwise the
sum depends on the order of addition.
Joe



David Winsemius <dwinsemius at comcast.net>
Sent by: r-help-bounces at r-project.org
02/15/2011 09:17 AM

To
Kjetil Halvorsen <kjetilbrinchmannhalvorsen at gmail.com>
cc
r-help at r-project.org, Maithula Chandrashekhar
<m.chandrashekhar1977 at gmail.com>
Subject
Re: [R] A Math question







On Feb 14, 2011, at 7:33 PM, Kjetil Halvorsen wrote:

> or even better:
>
> http://mathoverflow.net/

I beg to differ. That is designated in its FAQ as expecting "research
level questions", while the forum I offered is labeled as "Welcome to
Q&A for people studying math at any level and professionals in related
fields". I don't think the proffered question could be considered
"research level".

>
> On Sun, Feb 13, 2011 at 8:02 PM, David Winsemius <dwinsemius at comcast.net

> > wrote:
>>
>> On Feb 13, 2011, at 4:47 PM, Maithula Chandrashekhar wrote:
>>
>>> Dear all, I admit this is not anything to do R and even with
>>> Statistics perhaps. Strictly speaking this is a math related
>>> question.
>>> However I have some reasonable feeling that experts here would
>>> come up
>>> with some elegant suggestion to my question.
>>>
>>> Here my question is: What is sum of all Integers? I somewhere heard
>>> that it is Zero as positive and negative integers will just cancel
>>> each other out. However want to know is it correct?
>>
>> There are more appropriate places to pose such questions:
>> http://math.stackexchange.com/
>>

David Winsemius, MD
West Hartford, CT

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